why is the magnetic field most uniform when the distance between two coils is r

Answer:

v=wavelength x f = 2 x 3 = 6 m/s

Explanation:

The speed of a wave is the product of its frequency and wavelength. The speed of the periodic wave with the frequency of 3 Hz and wavelength of 2 m is 6 m/s.

Frequency of a wave is the number of wave cycles per unit time. It is the inverse of the time period of the wave. Frequency is inversely proportional to the wavelength  of the wave.

The relation between speed, frequency and wavelength of a wave is given by the expression as written below:

c =νλ

where, c is the speed, ν be the frequency and λ be the wavelength.

Given that ν = 3 Hz or 3 s⁻¹

and λ = 2 m

then speed c = 2 m × 3 Hz = 6 m/s

Therefore, the speed of the periodic wave is 6 m/s.

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The wavelength of microwaves with a frequency of 10 GHz is 0.03 meters or 3 centimeters. These microwaves cause the water molecules in the burrito to vibrate due to the absorption of their energy, resulting in the heating of the food.

The wavelength of microwaves with a frequency of 10 GHz can be calculated using the formula λ = c/f, where λ represents wavelength, c is the speed of light (3 × 10^8 m/s), and f is the frequency (10^10 Hz). Therefore, the wavelength of these microwaves is 0.03 meters or 3 centimeters.

The relationship between wavelength, frequency, and the speed of light is given by the equation λ = c/f, where λ represents wavelength, c is the speed of light, and f is the frequency. In this case, we have a frequency of 10 GHz, which is equivalent to 10^10 Hz. Plugging these values into the equation, we get:

λ = c/f

= (3 × 10^8 m/s) / (10^10 Hz)

= 3 × 10^(-2) meters

= 0.03 meters

= 3 centimeters

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Answer:

Se obtienen 2,27 gramos de metanol.

Explanation:

La reacción entre monóxido de carbono e hidrógeno para producir metanol es la siguiente:

CO + 2H₂ → CH₃OH  

Para encontrar el reactivo limitante y el reactivo en exceso, debemos calcular el número de moles de CO y H₂:

[tex]\eta_{CO} = \frac{m}{M} [/tex]              

En donde:    

m: es la masa

M: es el peso molecular  

[tex]\eta_{CO} = \frac{m}{M_{CO}} = \frac{2,0 g}{28,01 g/mol} = 0,071 moles [/tex]

[tex]\eta_{H_{2}} = \frac{2,0 g}{2,02 g/mol} = 0,99 moles [/tex]

Dado que la relación estequiométrica entre CO y H₂ es 1:2, el número de moles de hidrógeno gaseoso que reaccionan con el monóxido de carbono es:

[tex] \eta_{H_{2}} = \frac{2}{1}*0,071 = 0,142 moles [/tex]      

Entonces, se necesitan 0,142 moles de H₂ para reaccionar con 0,071 moles de CO y debido a que se tienen más moles de H₂ (0,99 moles) entonces el reactivo limitante es CO y el reactivo en exceso es H₂.

Ahora podemos encontar la masa de metanol obtenida usando el reactivo limitante (CO) y sabiendo que la realcion estequiométrica entre CO y CH₃OH es 1:1.    

[tex] \eta_{CH_{3}OH} = \eta_{CO} = 0,071 moles [/tex]

[tex] m = 0,071 moles*32,04 g/mol = 2,27 g [/tex]

Por lo tanto, se obtienen 2,27 gramos de metanol.

Espero que te sea de utilidad!      

Answer:

true:)

Explanation:

The decay of uranium isotopes is used to provide information about the age of earth.

Answer:

960 Watt

Explanation:

From the question,

Electric power = Voltage squared/Resistance

P = V²/R ..................... Equation 1

Where P = power, V = Voltage, R = Resistance

Given: V = 120 volts, R = 15 ohms.

Substitute these values into equation 1

P = 120²/15

P = 14400/15

P = 960 Watt

The female whale is approximately 3,000 meters away from the male whale.

To calculate the distance between the male and female blue whales, we can use the formula:

Distance = (Speed of sound in water × Time) / 2

Given that the speed of sound in water is approximately 1,500 m/s and the time taken for the sound to return is 4 seconds, we can substitute these values into the formula:

Distance = (1,500 m/s × 4 s) / 2

Simplifying the equation:

Distance = (6,000 m) / 2

Distance = 3,000 m

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The satellites that appear (from earth) to remain stationary over a given spot are called stationary satellites. They are also known as geostationary satellites. These types of satellites travel at a speed and direction that keeps pace with the earth’s rotation. This enables them to stay in a fixed position relative to the earth's surface at all times. They are commonly used for telecommunications, weather forecasting, and remote sensing applications.

A geostationary orbit is an orbit that is located directly above the equator and follows the direction of Earth's rotation. This type of orbit is around 36,000 km above Earth's surface. Satellites in this orbit have an orbital period of exactly one day, which is the same as the time it takes for the Earth to complete one rotation on its axis.A geostationary satellite is essentially a specialized communications satellite that remains stationary in the sky relative to a specific location on Earth's surface. This allows it to provide continuous coverage to that location, making it ideal for applications such as television broadcasting, weather forecasting, and remote sensing. In conclusion, geostationary or stationary satellites travel at a speed and direction that keeps pace with the earth’s rotation, so they appear (from earth) to remain stationary over a given spot.

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Answer:223.46 MJ

Explanation:

Given

The thermal conductivity of brick wall is [tex]k=1.16\ W/m.^{\circ}C[/tex]

Cross-section of Wall [tex]A=5\m \times 7\ m[/tex]

time period [tex]t=17.2\ h=17.2\times 60\times 60=61,920\ s[/tex]

Inside temperature [tex]T_i=24^{\circ}C[/tex]

Outside temperature [tex]T_o=8^{\circ}C[/tex]

Heat transfer through the bricks

[tex]\dot{Q}=kA\dfrac{dT}{dx}[/tex]

[tex]\dot{Q}=1.16\times 35\times \dfrac{16}{0.18}\\\\\dot{Q}=3608.88\ W[/tex]

Heat flow for 17.2 h

[tex]Q=3608.88\times 61,920=223.46\ MJ[/tex]

A. Symbolic equation for the location of the center of mass of the three beads relative to the left end of the rodIn order to find the center of mass, we need to use the formula:

[tex](M1x1 + M2x2 + M3x3) / M\\where\\M \\ =\\ m1 + m2 + m3M1 = m1M2 = \\m2M3 = m3x1 \\= d1x2 = d1 + d2x3 = d1 + d2 + d3\\\\Now, we have\\\\M1x1 + M2x2 + M3x3 = 27 × 0.013 + 14 × 0.032 + 49 × 0.062 \\= 0.1310M \\= m1 + m2 + m3 \\= 27 + 14 + 49 = 90[/tex]

The location of the center of mass is given

[tex]asx = (M1x1 + M2x2 + M3x3) / M = 0.1310 / 90= 0.00146 cmB.[/tex]

Find the center of mass in centimeters relative to the left end of the rodThe center of mass is located at a distance of 0.00146 cm relative to the left end of the rod.C. Symbolic equation for the location of the center of mass of the three beads relative to the center beadWe need to find the distance between the center bead and the center of mass.Let d = distance between center bead and the center of mass.

Find the center of mass in centimeters relative to the middle beadFrom the above equation in part C, we know

[tex]x2 + d = 0.1304[/tex]

Let's calculate the distance between center bead and the center of mass,

[tex]d = x - x2 = 0.00146 cm[/tex]

Now, we can find the center of mass in centimeters relative to the middle bead asx - x2 = 0.00146 cmThe center of mass is 0.00146 cm away from the middle bead.

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Explanation:

With most of our blue planet covered by water, it's little wonder that, centuries ago, the oceans were believed to hide mysterious creatures including sea serpents and mermaids. Merfolk (mermaids and mermen) are, of course, the marine version of half-human, half-animal legends that have captured human imagination for ages. One source, the "Arabian Nights," described mermaids as having "moon faces and hair like a woman's but their hands and feet were in their bellies and they had tails like fishes."

C.J.S. Thompson, a former curator at the Royal College of Surgeons of England, notes in his book "The Mystery and Lore of Monsters" that "Traditions concerning creatures half-human and half-fish in form have existed for thousands of years, and the Babylonian deity Era or Oannes, the Fish-god ... is usually depicted as having a bearded head with a crown and a body like a man, but from the waist downwards he has the shape of a fish." Greek mythology contains stories of the god Triton, the merman messenger of the sea, and several modern religions including Hinduism and Candomble (an Afro-Brazilian belief) worship mermaid goddesses to this day.

When light travels from air into water through an oil film, several optical phenomena come into play: refraction, reflection, and interference.

First, refraction occurs at the air-water interface. As light enters the water, it undergoes a change in speed and direction due to the change in the refractive index between the two mediums. This causes the light to bend or deviate from its original path. Next, reflection occurs at the interface between the water and the oil film. A portion of the light is reflected back into the water, following the law of reflection. The angle of incidence is equal to the angle of reflection.

Interference also plays a role in this scenario. When the light waves reflect off the oil film, they can interfere constructively or destructively depending on their phase relationship. This interference can result in the appearance of colorful patterns, commonly known as thin-film interference. The colors observed in the oil film are due to the constructive and destructive interference of different wavelengths of light. The thickness of the oil film determines which wavelengths interfere constructively and produce visible colors.

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Answer:There are two main types of friction, static friction and kinetic friction. Static friction operates between two surfaces that aren't moving relative to each other, while kinetic friction acts between objects in motion.

(a) To find the total translational kinetic energy of the gas molecules, we can use the formula: Total kinetic energy = (3/2) * N * k * T, Where: N = Avogadro's number, k = Boltzmann's constant, T = temperature in Kelvin

First, let's convert the given mass of hydrogen gas (2.0 g) into moles: Number of moles = mass / molar mass Number of moles = 2.0 g / (2.016 g/mol) ≈ 0.993 mol. Next, we need to convert the temperature in Kelvin. Since only the rms speed is provided, we can use the following equation to relate it to temperature: v(rms) = sqrt((3 * k * T) / ms. where: v(rms) = rms speed m = molar mass of the gas. Rearranging the equation, we can solve for T: T = (m * v(rms)^2) / (3 * k) Using the given rms speed of 1600 m/s and the molar mass of hydrogen gas (2.016 g/mol), we can calculate the temperature in Kelvin: T = (2.016 g/mol * (1600 m/s)^2) / (3 * (1.381 × 10^-23 J/K)) Calculating T, we find: T ≈ 7309 K. Now, we can substitute the values into the formula for total kinetic energy: Total kinetic energy = (3/2) * N * k * T Total kinetic energy = (3/2) * (0.993 mol) * (1.381 × 10^-23 J/K) * (7309 K) Calculating the total kinetic energy, we find: Total kinetic energy ≈ 2.676 × 10^-19 J, Therefore, the total translational kinetic energy of the gas molecules is approximately 2.676 × 10^-19 J. (b) The thermal energy of the gas is equal to the total translational kinetic energy since we assume the gas is monoatomic and all its energy is in the form of kinetic energy. So, the thermal energy is also approximately 2.676 × 10^-19 J. (c) To find the new rms speed of the molecules after the work and heat transfer, we can use the principle of conservation of energy: Change in thermal energy = Work done + Heat transferred. Since the change in thermal energy is given as 1200 J, we have: 1200 J = 500 J + Heat transferred. Heat transferred = 1200 J - 500 J Heat transferred = 700 J Now, we can use the equation v(rms) = sqrt((3 * k * T) / m) to find the new rms speed. Rearranging the equation, we have: v(rms) = sqrt((3 * k * T') / m) Where T' is the new temperature in Kelvin. We can solve for T' by rearranging the equation: T' = (m * v(rms)^2) / (3 * k) Substituting the values into the equation, we have: T' = (2.016 g/mol * (1600 m/s)^2) / (3 * (1.381 × 10^-23 J/K)) Calculating T', we find: T' ≈ 7309 K, Therefore, the rms speed of the molecules after the work and heat transfer is approximately 1600 m/s, the same as before.

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Answer:

1-B, 2-A, 3-D, 4-C

Explanation:

1. The force exerted is, F = 35 N

  Distance the box is moved, d = 4 m

  So the amount of work done is, W = F x d

                                                            = 35 x 4

                                                            = 140 Newton-meters

2. Work done, W  = 420 Nm

   Time, T = 3 seconds

   Therefore, the power required is,

   [tex]$P=\frac{W}{T}$[/tex]

   [tex]$P=\frac{420}{3}$[/tex]

       = 140 joules

3. The force exerted is, F = 1.2 N

  Distance the box is moved, d = 5 m

  So the amount of work done is, W = F x d

                                                            = 1.2 x 5

                                                            = 6 Newton-meters

4. Work done, W  = 120 Nm

   Time, T = 20 seconds

   Therefore, the power required is,

   [tex]$P=\frac{W}{T}$[/tex]

   [tex]$P=\frac{120}{20}$[/tex]

       = 6 joules

Part A :The position of the particle in vector form is given by[tex]r⃗ (t)=R[cos(ωt)i^+sin(ωt)j^][/tex]where R is the radius of the circle and ω is the angular velocity.The velocity of the particle is given by taking the derivative of the position vector with respect to time.

Taking derivative with respect to time on both side we get [tex]v⃗ (t)=d/dt R[cos(ωt)i^+sin(ωt)j^]= R[-in(ωt)ωi^+cos(ωt)ωj^]=ωR[-sin(ωt)i^+cos(ωt)j^]v⃗ (t)=ωR[-sin(ωt)i^+cos(ωt)j^][/tex]Thus the velocity of the mass at a time t is given by [tex]v⃗ (t)=ωR[-sin(ωt)i^+cos(ωt)j^][/tex].

Part B :

We have to find the velocity at time -t. The velocity of the particle is given by taking the derivative of the position vector with respect to time. Thus the velocity of the mass at a time -t is given by [tex]v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^][/tex]

[tex]v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^][/tex]Part C :

The average acceleration of the particle can be computed using the formulaa = [tex]Δv/Δt[/tex]The velocity at time t is given by[tex]v⃗ (t) = ωR[-sin(ωt)i^+cos(ωt)j^][/tex]

The velocity at time -t is given by [tex]v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^][/tex]

[tex]v⃗ (-t) = ωR[sin(ωt)i^ - cos(ωt)j^][/tex]The change in velocity over the interval from -t to t is therefore

[tex]Δv = v(t) - v(-t) = 2ωR[sin(ωt)i^ + cos(ωt)j^][/tex]

The time interval over which this change occurs is[tex]Δt = 2t[/tex]Thus the average acceleration of the particle is given by a = [tex]Δv/Δt = ω^2R[sin(ωt)i^ + cos(ωt)j^]/t[/tex]

[tex]a = Δv/Δt = ω^2R[sin(ωt)i^ + cos(ωt)j^]/t[/tex]

The acceleration can be expressed in terms of R, ω, t, and the unit vectors [tex]i^ and j^[/tex] as [tex]a = ω^2R[sin(ωt)i^ + cos(ωt)j^]/t[/tex].

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Answer:

they all need a source of oxygen

Answer:

B

Explanation:

Answer:

13,308 MAYBE IF IT ISN'T IM SO SORRY

Explanation:

Answer:

the velocity component parallel to the magnetic field vector

Explanation:

When a charged particle moves in a helical path, we can decompose its velocity into two parts v_parallel and v_perpendicular to the magnetic field.

Let's analyze which component receives a force

            F = q vxB

the bold letters indicate vectors, in the vector product if the two vectors are parallel the angle is zero and the sin 0 = 0 for which there is no force. therefore the velocity parallel to the field remains constant

If the two vectors are perpendicular, the angle is 90º and the sin 90 = 1, for which there is a force, which has a radial direction and consequently a centripetal acceleration that gives a circular path that does not remove the particle from the magnetic field

When checking the different answers, the correct one is: the velocity component parallel to the magnetic field vector

The frequency of light with a wavelength of 400 nm is approximately [tex]7.494 * 10^{14} Hz[/tex] (or 749.4 THz).

To calculate the frequency of light, you can use the equation:

Frequency = Speed of light / Wavelength

The speed of light in a vacuum is approximately 299,792,458 meters per second (m/s). We need to convert the given wavelength of 400 nm to meters.

[tex]1 nm = 1 * 10^{-9}[/tex] meters

Converting 400 nm to meters:

[tex]400 nm = 400 * 10^{-9} meters = 4 * 10^{-7} meters[/tex]

Now, we can calculate the frequency:

Frequency = (Speed of light) / (Wavelength)

[tex]= 299,792,458 m/s / (4 * 10^{-7} meters)\\ =7.494 * 10^{14} Hz[/tex]

Therefore, the frequency of light with a wavelength of 400 nm is approximately [tex]7.494 * 10^{14} Hz[/tex] (or 749.4 THz).

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A balanced equation is a chemical equation in which the number of atoms of each element on both sides of the equation is equal. It represents a chemical reaction, indicating the reactants and products involved and the stoichiometric relationship between them.

The balanced equation for the reaction between RbNO3 and BeF2 is: 2RbNO3 + BeF2 → Be(NO3)2 + 2RbF.

To check if the equation is balanced or not, we can count the number of atoms of each element on both sides of the equation.

Here, we have Rb: 2 on both sides,  N: 2 on both sides, O: 6 on both sides, Be: 1 on both sides, F: 2 on both sides.

Therefore, the balanced equation for the reaction between RbNO3 and BeF2 is 2RbNO3 + BeF2 → Be(NO3)2 + 2RbF, which has the correct products for the given reactants.

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Answer:

1.17 m

Explanation:

From the question,

s₁ = vt₁/2................ Equation 1

Where s₁ = distance of the reflecting object for the first echo, v = speed of the sound in air, t₁ = time to dectect the first echo.

Given: v = 343 m/s, t = 0.0115 s

Substitute into equation 1

s₁ = (343×0.0115)/2

s₁ = 1.97 m.

Similarly,

s₂ = vt₂/2.................. Equation 2

Where s₂ = distance of the reflecting object for the second echo, t₂ = Time taken to detect the second echo

Given: v = 343 m/s, t₂ = 0.0183 s

Substitute into equation 2

s₂ = (343×0.0183)/2

s₂ = 3.14 m

The distance moved by the reflecting object from s₁ to s₂ = s₂-s₁

s₂-s₁ =  (3.14-1.97) m = 1.17 m

Kinetic energy refers to the energy possessed by an object due to its motion. The formula for kinetic energy is given as follows: Kinetic energy = 1/2 × mass × velocity², Where: mass = the mass of the object, velocity = the speed of the object.

We can equate the kinetic energies of the car and truck using the formula above. Let's assume that the speed of the car is v. Therefore, we can write:1/2 × 1800 × v² = 1/2 × 1.80×10⁴ × (25/3.6)², Where:25/3.6 is used to converting the speed of the truck from km/h to m/s.

Simplifying the right-hand side of the equation, we get:1/2 × 1.80×10⁴ × (25/3.6)² = 781250 J.

Now, we can solve for v by dividing both sides of the equation by 1/2 × 1800:1/2 × 1800 × v² = 781250v² = 781250 ÷ 900v² = 868.056v ≈ 29.47 m/s.

Therefore, the speed at which an 1800 kg compact car has the same kinetic energy as a 1.80×10⁴ kg truck going 25.0 km/h is approximately 29.47 m/s.

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When the given alkene is treated with MCPBA (meta-chloroperoxybenzoic acid), four stereoisomers are formed due to the presence of a double bond.

These stereoisomers can be classified as cis-trans isomers and enantiomers. When an alkene reacts with MCPBA, it undergoes an epoxidation reaction, resulting in the formation of an epoxide. The given alkene has a double bond between two carbon atoms, and MCPBA adds an oxygen atom across this double bond, forming an epoxide.

The first type of stereoisomer formed is the cis-trans isomers. The cis isomer refers to the arrangement where the two substituents on the same side of the double bond in the alkene remain on the same side in the resulting epoxide. The trans isomer refers to the arrangement where the substituents on the alkene's two carbons switch sides in the resulting epoxide. Thus, two cis-trans isomers are formed.

The second type of stereoisomer formed is enantiomers. Enantiomers are non-superimposable mirror images of each other. In the case of the given alkene, if the substituents attached to the double bond are different, two enantiomers are formed as a result of the epoxidation reaction.

In total, four stereoisomers are formed when the given alkene is treated with MCPBA. These stereoisomers can be identified by their different arrangements of substituents around the newly formed epoxide group.

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Answer:

3 moles

Explanation:

Ratio of O2 to CO2 = 2 : 1 = 6 : 3

Answer:

12000N

Explanation:

gravity on earth is six times one on the moon

To observe asteroids: Calculate and improve orbits. Know about asteroids. Identify characteristics of asteroids. Take samples from asteroids. Identify asteroids a threat to life on earth. The correct answers are A, B, C, D, and E.

Observing asteroids allows us to:

A. Calculate and improve current calculations of their orbits: By observing their positions and movements over time, we can refine our understanding of their orbits, predict future positions, and assess potential collision risks.

B. Know more about the composition of asteroids: By analyzing their reflected light, emission spectra, and studying meteorites that originate from asteroids, we can gain insights into their mineralogical and chemical compositions, helping us understand the formation and evolution of the solar system.

C. Identify characteristics of asteroids such as if they have rings or tails: Through careful observations, we can detect features like rings or tails associated with certain asteroids, providing valuable information about their structure and behavior.

D. Take samples of materials from asteroids: By sending spacecraft missions to asteroids, we can collect samples from their surfaces or even perform asteroid deflection experiments, enabling us to study their physical properties and potential resources.

E. Identify asteroids that represent a threat to life on Earth: Continuous monitoring and observation of asteroids allow us to identify and track potentially hazardous asteroids that may pose a risk of impacting Earth, enabling us to plan and develop mitigation strategies if necessary.

Therefore, observing asteroids contributes to a wide range of activities, from refining orbital calculations and understanding their composition and characteristics to assessing potential threats and even collecting samples from them.The correct answers are A, B, C, D, and E.

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When the average velocity is 2.4 m/s, the horizontal 0.35 meter diameter cast iron water pipe experiences a pressure drop (P) of roughly 16457.14 kPa every 100 meters.

To determine the pressure drop per 100-meter length of a horizontal 0.35-meter diameter cast iron water pipe, we can use the Darcy-Weisbach equation. The equation is as follows:

[tex]\begin{equation}\Delta P = \frac{f \cdot \frac{L}{D} \cdot (\rho \cdot V^2)}{2}[/tex]

where ΔP is the pressure drop, f is the Darcy friction factor, L is the length of the pipe (100 meters in this case), D is the diameter of the pipe (0.35 meters), ρ is the density of water, and V is the average velocity of water.

To calculate the pressure drop, we need to determine the Darcy friction factor. For a rough cast iron pipe, we can estimate the friction factor to be around 0.02.

Using the given values and the estimated friction factor, the calculation becomes:

[tex]\begin{equation}\Delta P = \frac{0.02 \cdot \frac{100}{0.35} \cdot (\rho \cdot 2.4^2)}{2}[/tex]

Since the density of water (ρ) is approximately 1000 kg/m³, we can substitute this value and calculate the pressure drop:

ΔP = [tex]\frac{0.02 \times \frac{100}{0.35} \times 1000 \times 2.4^2}{2}[/tex]

Let's solve the expression to calculate the pressure drop (ΔP) in kilopascals (kPa):

ΔP =  [tex]\frac{0.02 \times \frac{100}{0.35} \times 1000 \times 2.4^2}{2}[/tex]

First, let's simplify the expression:

ΔP = [tex]\frac{0.02 \times (285.714) \times (1000 \times 5.76)}{2}[/tex]

   = 16457.14

Therefore, the pressure drop (ΔP) per 100-meter length of the horizontal 0.35-meter diameter cast iron water pipe, when the average velocity is 2.4 m/s, is approximately 16457.14 kPa.

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Complete question :

Determine the pressure drop per 100 -m length of horizontal new 0.35−m-diameter cast iron water pipe when the average velocity 2.4 m/s. Δp= kPa

The maximum velocity of the particle is 100 m/s. Negative sign indicates that the velocity is in the opposite direction of the displacement at that particular point in time.

To find the maximum velocity of a particle in simple harmonic motion, we need to differentiate the position function with respect to time and then find the maximum value of the resulting velocity function.

Given the position function x = 2cos(50t), we can find the velocity function v(t) by taking the derivative of x with respect to t:

v(t) = dx/dt = -2(50)sin(50t) = -100sin(50t)

The maximum velocity occurs when the sine function has a maximum value of 1. Therefore, the maximum velocity can be found by evaluating the velocity function at that point. In this case, the maximum value of sin(50t) is 1 when 50t = π/2 or t = π/100.

Substituting t = π/100 into the velocity function:

v_max = -100sin(50(π/100)) = -100sin(π/2) = -100(1) = -100 m/s

Therefore, the maximum velocity of the particle is 100 m/s. Note that the negative sign indicates that the velocity is in the opposite direction of the displacement at that particular point in time.

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